{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<!--BOOK_INFORMATION-->\n",
    "<img align=\"left\" style=\"padding-right:10px;\" src=\"figures/PDSH-cover-small.png\">\n",
    "\n",
    "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n",
    "\n",
    "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<!--NAVIGATION-->\n",
    "< [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb) | [Contents](Index.ipynb) | [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb) >\n",
    "\n",
    "<a href=\"https://colab.research.google.com/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/05.09-Principal-Component-Analysis.ipynb\"><img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open and Execute in Google Colaboratory\"></a>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  In Depth: Principal Component Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Up until now, we have been looking in depth at supervised learning estimators: those estimators that predict labels based on labeled training data.\n",
    "Here we begin looking at several unsupervised estimators, which can highlight interesting aspects of the data without reference to any known labels.\n",
    "\n",
    "In this section, we explore what is perhaps one of the most broadly used of unsupervised algorithms, principal component analysis (PCA).\n",
    "PCA is fundamentally a dimensionality reduction algorithm, but it can also be useful as a tool for visualization, for noise filtering, for feature extraction and engineering, and much more.\n",
    "After a brief conceptual discussion of the PCA algorithm, we will see a couple examples of these further applications.\n",
    "\n",
    "We begin with the standard imports:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns; sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Introducing Principal Component Analysis\n",
    "\n",
    "Principal component analysis is a fast and flexible unsupervised method for dimensionality reduction in data, which we saw briefly in [Introducing Scikit-Learn](05.02-Introducing-Scikit-Learn.ipynb).\n",
    "Its behavior is easiest to visualize by looking at a two-dimensional dataset.\n",
    "Consider the following 200 points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
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/jxHYwOAjqDHkRDMKOPT5Z0/PF/JueOGQ1K6DB0eqqCj8M9LQz06blidpjd55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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x101eb9f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(1)\n",
    "X = np.dot(rng.rand(2, 2), rng.randn(2, 200)).T\n",
    "plt.scatter(X[:, 0], X[:, 1])\n",
    "plt.axis('equal');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "By eye, it is clear that there is a nearly linear relationship between the x and y variables.\n",
    "This is reminiscent of the linear regression data we explored in [In Depth: Linear Regression](05.06-Linear-Regression.ipynb), but the problem setting here is slightly different: rather than attempting to *predict* the y values from the x values, the unsupervised learning problem attempts to learn about the *relationship* between the x and y values.\n",
    "\n",
    "In principal component analysis, this relationship is quantified by finding a list of the *principal axes* in the data, and using those axes to describe the dataset.\n",
    "Using Scikit-Learn's ``PCA`` estimator, we can compute this as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, n_components=2, whiten=False)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=2)\n",
    "pca.fit(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The fit learns some quantities from the data, most importantly the \"components\" and \"explained variance\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.94446029  0.32862557]\n",
      " [ 0.32862557 -0.94446029]]\n"
     ]
    }
   ],
   "source": [
    "print(pca.components_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.75871884  0.01838551]\n"
     ]
    }
   ],
   "source": [
    "print(pca.explained_variance_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "To see what these numbers mean, let's visualize them as vectors over the input data, using the \"components\" to define the direction of the vector, and the \"explained variance\" to define the squared-length of the vector:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OR+h135AGgIceeghGoxEAsHjxYhw/flxRUGdlmYb9DLGeRoJ1pcxEqacTJ9qg1xdCrw+8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\nY1ATEREJjEFNREQkMAY1ERGRwP4/bV+C7ucCrxYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118c75cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def draw_vector(v0, v1, ax=None):\n",
    "    ax = ax or plt.gca()\n",
    "    arrowprops=dict(arrowstyle='->',\n",
    "                    linewidth=2,\n",
    "                    shrinkA=0, shrinkB=0)\n",
    "    ax.annotate('', v1, v0, arrowprops=arrowprops)\n",
    "\n",
    "# plot data\n",
    "plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
    "for length, vector in zip(pca.explained_variance_, pca.components_):\n",
    "    v = vector * 3 * np.sqrt(length)\n",
    "    draw_vector(pca.mean_, pca.mean_ + v)\n",
    "plt.axis('equal');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "These vectors represent the *principal axes* of the data, and the length of the vector is an indication of how \"important\" that axis is in describing the distribution of the data—more precisely, it is a measure of the variance of the data when projected onto that axis.\n",
    "The projection of each data point onto the principal axes are the \"principal components\" of the data.\n",
    "\n",
    "If we plot these principal components beside the original data, we see the plots shown here:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "![](figures/05.09-PCA-rotation.png)\n",
    "[figure source in Appendix](06.00-Figure-Code.ipynb#Principal-Components-Rotation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This transformation from data axes to principal axes is an *affine transformation*, which basically means it is composed of a translation, rotation, and uniform scaling.\n",
    "\n",
    "While this algorithm to find principal components may seem like just a mathematical curiosity, it turns out to have very far-reaching applications in the world of machine learning and data exploration."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### PCA as dimensionality reduction\n",
    "\n",
    "Using PCA for dimensionality reduction involves zeroing out one or more of the smallest principal components, resulting in a lower-dimensional projection of the data that preserves the maximal data variance.\n",
    "\n",
    "Here is an example of using PCA as a dimensionality reduction transform:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original shape:    (200, 2)\n",
      "transformed shape: (200, 1)\n"
     ]
    }
   ],
   "source": [
    "pca = PCA(n_components=1)\n",
    "pca.fit(X)\n",
    "X_pca = pca.transform(X)\n",
    "print(\"original shape:   \", X.shape)\n",
    "print(\"transformed shape:\", X_pca.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The transformed data has been reduced to a single dimension.\n",
    "To understand the effect of this dimensionality reduction, we can perform the inverse transform of this reduced data and plot it along with the original data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6XS5oaZVMpDEF9datWzn33HMBOO2003jjjTd6n6utraWiooJgMAjA6aefzpYt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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11920e438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = pca.inverse_transform(X_pca)\n",
    "plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
    "plt.scatter(X_new[:, 0], X_new[:, 1], alpha=0.8)\n",
    "plt.axis('equal');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The light points are the original data, while the dark points are the projected version.\n",
    "This makes clear what a PCA dimensionality reduction means: the information along the least important principal axis or axes is removed, leaving only the component(s) of the data with the highest variance.\n",
    "The fraction of variance that is cut out (proportional to the spread of points about the line formed in this figure) is roughly a measure of how much \"information\" is discarded in this reduction of dimensionality.\n",
    "\n",
    "This reduced-dimension dataset is in some senses \"good enough\" to encode the most important relationships between the points: despite reducing the dimension of the data by 50%, the overall relationship between the data points are mostly preserved."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### PCA for visualization: Hand-written digits\n",
    "\n",
    "The usefulness of the dimensionality reduction may not be entirely apparent in only two dimensions, but becomes much more clear when looking at high-dimensional data.\n",
    "To see this, let's take a quick look at the application of PCA to the digits data we saw in [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb).\n",
    "\n",
    "We start by loading the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "digits = load_digits()\n",
    "digits.data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Recall that the data consists of 8×8 pixel images, meaning that they are 64-dimensional.\n",
    "To gain some intuition into the relationships between these points, we can use PCA to project them to a more manageable number of dimensions, say two:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1797, 64)\n",
      "(1797, 2)\n"
     ]
    }
   ],
   "source": [
    "pca = PCA(2)  # project from 64 to 2 dimensions\n",
    "projected = pca.fit_transform(digits.data)\n",
    "print(digits.data.shape)\n",
    "print(projected.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We can now plot the first two principal components of each point to learn about the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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62XbkD8PoD6vbdkVXwcw4S3oO0tOxjxEjwtiyNogE8CslgkIQNSz0UDNhexK/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K5QJ0cLtaiwYOUp22UCWgAn6TLePsCtE58CoP3KRUeb0d1pTrw2BcDciQLSha6r61GFyifVu3jB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\n5p577mPr1o+Jj0+IrIcKgnDxRGo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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1195ba048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(projected[:, 0], projected[:, 1],\n",
    "            c=digits.target, edgecolor='none', alpha=0.5,\n",
    "            cmap=plt.cm.get_cmap('spectral', 10))\n",
    "plt.xlabel('component 1')\n",
    "plt.ylabel('component 2')\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Recall what these components mean: the full data is a 64-dimensional point cloud, and these points are the projection of each data point along the directions with the largest variance.\n",
    "Essentially, we have found the optimal stretch and rotation in 64-dimensional space that allows us to see the layout of the digits in two dimensions, and have done this in an unsupervised manner—that is, without reference to the labels."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### What do the components mean?\n",
    "\n",
    "We can go a bit further here, and begin to ask what the reduced dimensions *mean*.\n",
    "This meaning can be understood in terms of combinations of basis vectors.\n",
    "For example, each image in the training set is defined by a collection of 64 pixel values, which we will call the vector $x$:\n",
    "\n",
    "$$\n",
    "x = [x_1, x_2, x_3 \\cdots x_{64}]\n",
    "$$\n",
    "\n",
    "One way we can think about this is in terms of a pixel basis.\n",
    "That is, to construct the image, we multiply each element of the vector by the pixel it describes, and then add the results together to build the image:\n",
    "\n",
    "$$\n",
    "{\\rm image}(x) = x_1 \\cdot{\\rm (pixel~1)} + x_2 \\cdot{\\rm (pixel~2)} + x_3 \\cdot{\\rm (pixel~3)} \\cdots x_{64} \\cdot{\\rm (pixel~64)}\n",
    "$$\n",
    "\n",
    "One way we might imagine reducing the dimension of this data is to zero out all but a few of these basis vectors.\n",
    "For example, if we use only the first eight pixels, we get an eight-dimensional projection of the data, but it is not very reflective of the whole image: we've thrown out nearly 90% of the pixels!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "source": [
    "![](figures/05.09-digits-pixel-components.png)\n",
    "[figure source in Appendix](06.00-Figure-Code.ipynb#Digits-Pixel-Components)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The upper row of panels shows the individual pixels, and the lower row shows the cumulative contribution of these pixels to the construction of the image.\n",
    "Using only eight of the pixel-basis components, we can only construct a small portion of the 64-pixel image.\n",
    "Were we to continue this sequence and use all 64 pixels, we would recover the original image."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "But the pixel-wise representation is not the only choice of basis. We can also use other basis functions, which each contain some pre-defined contribution from each pixel, and write something like\n",
    "\n",
    "$$\n",
    "image(x) = {\\rm mean} + x_1 \\cdot{\\rm (basis~1)} + x_2 \\cdot{\\rm (basis~2)} + x_3 \\cdot{\\rm (basis~3)} \\cdots\n",
    "$$\n",
    "\n",
    "PCA can be thought of as a process of choosing optimal basis functions, such that adding together just the first few of them is enough to suitably reconstruct the bulk of the elements in the dataset.\n",
    "The principal components, which act as the low-dimensional representation of our data, are simply the coefficients that multiply each of the elements in this series.\n",
    "This figure shows a similar depiction of reconstructing this digit using the mean plus the first eight PCA basis functions:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "source": [
    "![](figures/05.09-digits-pca-components.png)\n",
    "[figure source in Appendix](06.00-Figure-Code.ipynb#Digits-PCA-Components)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Unlike the pixel basis, the PCA basis allows us to recover the salient features of the input image with just a mean plus eight components!\n",
    "The amount of each pixel in each component is the corollary of the orientation of the vector in our two-dimensional example.\n",
    "This is the sense in which PCA provides a low-dimensional representation of the data: it discovers a set of basis functions that are more efficient than the native pixel-basis of the input data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Choosing the number of components\n",
    "\n",
    "A vital part of using PCA in practice is the ability to estimate how many components are needed to describe the data.\n",
    "This can be determined by looking at the cumulative *explained variance ratio* as a function of the number of components:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1PDrYVUoJ4UF+7i6FiIioxfDIYBdC4FJZTd3DXxR8+AsREVE9jwz2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\nJCMMdiIiIhlhsBMREckIg52IiEhG/j/X1c1dl6Mg0gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11942e3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA().fit(digits.data)\n",
    "plt.plot(np.cumsum(pca.explained_variance_ratio_))\n",
    "plt.xlabel('number of components')\n",
    "plt.ylabel('cumulative explained variance');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This curve quantifies how much of the total, 64-dimensional variance is contained within the first $N$ components.\n",
    "For example, we see that with the digits the first 10 components contain approximately 75% of the variance, while you need around 50 components to describe close to 100% of the variance.\n",
    "\n",
    "Here we see that our two-dimensional projection loses a lot of information (as measured by the explained variance) and that we'd need about 20 components to retain 90% of the variance.  Looking at this plot for a high-dimensional dataset can help you understand the level of redundancy present in multiple observations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## PCA as Noise Filtering\n",
    "\n",
    "PCA can also be used as a filtering approach for noisy data.\n",
    "The idea is this: any components with variance much larger than the effect of the noise should be relatively unaffected by the noise.\n",
    "So if you reconstruct the data using just the largest subset of principal components, you should be preferentially keeping the signal and throwing out the noise.\n",
    "\n",
    "Let's see how this looks with the digits data.\n",
    "First we will plot several of the input noise-free data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11969c908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_digits(data):\n",
    "    fig, axes = plt.subplots(4, 10, figsize=(10, 4),\n",
    "                             subplot_kw={'xticks':[], 'yticks':[]},\n",
    "                             gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
    "    for i, ax in enumerate(axes.flat):\n",
    "        ax.imshow(data[i].reshape(8, 8),\n",
    "                  cmap='binary', interpolation='nearest',\n",
    "                  clim=(0, 16))\n",
    "plot_digits(digits.data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now lets add some random noise to create a noisy dataset, and re-plot it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+fftkTbly5SLX/NMWLlzo5mqQq5keqtqjRw9Zo96fZmYNGzZ082LFismaRH36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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119676828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "noisy = np.random.normal(digits.data, 4)\n",
    "plot_digits(noisy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "It's clear by eye that the images are noisy, and contain spurious pixels.\n",
    "Let's train a PCA on the noisy data, requesting that the projection preserve 50% of the variance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(0.50).fit(noisy)\n",
    "pca.n_components_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Here 50% of the variance amounts to 12 principal components.\n",
    "Now we compute these components, and then use the inverse of the transform to reconstruct the filtered digits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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eAACQPDY8AAAgeWEsvVixYm49iu+qKF4UFz333HPduhr6ZmZWtWpVt75u3TrZ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\nAEgeGx4AAJA8NjwAACB5bHgAAEDy/gcjsffkWE6IPAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11976a358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "components = pca.transform(noisy)\n",
    "filtered = pca.inverse_transform(components)\n",
    "plot_digits(filtered)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This signal preserving/noise filtering property makes PCA a very useful feature selection routine—for example, rather than training a classifier on very high-dimensional data, you might instead train the classifier on the lower-dimensional representation, which will automatically serve to filter out random noise in the inputs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Example: Eigenfaces\n",
    "\n",
    "Earlier we explored an example of using a PCA projection as a feature selector for facial recognition with a support vector machine (see [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)).\n",
    "Here we will take a look back and explore a bit more of what went into that.\n",
    "Recall that we were using the Labeled Faces in the Wild dataset made available through Scikit-Learn:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Ariel Sharon' 'Colin Powell' 'Donald Rumsfeld' 'George W Bush'\n",
      " 'Gerhard Schroeder' 'Hugo Chavez' 'Junichiro Koizumi' 'Tony Blair']\n",
      "(1348, 62, 47)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import fetch_lfw_people\n",
    "faces = fetch_lfw_people(min_faces_per_person=60)\n",
    "print(faces.target_names)\n",
    "print(faces.images.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's take a look at the principal axes that span this dataset.\n",
    "Because this is a large dataset, we will use ``RandomizedPCA``—it contains a randomized method to approximate the first $N$ principal components much more quickly than the standard ``PCA`` estimator, and thus is very useful for high-dimensional data (here, a dimensionality of nearly 3,000).\n",
    "We will take a look at the first 150 components:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomizedPCA(copy=True, iterated_power=3, n_components=150,\n",
       "       random_state=None, whiten=False)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import RandomizedPCA\n",
    "pca = RandomizedPCA(150)\n",
    "pca.fit(faces.data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "In this case, it can be interesting to visualize the images associated with the first several principal components (these components are technically known as \"eigenvectors,\"\n",
    "so these types of images are often called \"eigenfaces\").\n",
    "As you can see in this figure, they are as creepy as they sound:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2nG544liMyEv71vue3z0380r1rnzpJgUQPC1V4s4GAc8Cc/x3+znwENr42U0B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lAB/bdyHVYWz156czNTnGEl8T0wjjrQYaLkqfk84Xw54XKecRlHGFAD5TztsGspSPuKfV+w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\nrdv6F1v/F1E+s8isuOd8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b4fb5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(3, 8, figsize=(9, 4),\n",
    "                         subplot_kw={'xticks':[], 'yticks':[]},\n",
    "                         gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
    "for i, ax in enumerate(axes.flat):\n",
    "    ax.imshow(pca.components_[i].reshape(62, 47), cmap='bone')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The results are very interesting, and give us insight into how the images vary: for example, the first few eigenfaces (from the top left) seem to be associated with the angle of lighting on the face, and later principal vectors seem to be picking out certain features, such as eyes, noses, and lips.\n",
    "Let's take a look at the cumulative variance of these components to see how much of the data information the projection is preserving:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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G0Wj0ZEnkJqcQyD9ajm92FWNfYQUAwKAPwC1XxyJpeC/ERBp8XCEREUnxaMjn5uYiKSkJ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\nMsWQJyIikimGPBERkUwx5ImIiGTq/wMjrvJM/BfyVgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b7c3630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.cumsum(pca.explained_variance_ratio_))\n",
    "plt.xlabel('number of components')\n",
    "plt.ylabel('cumulative explained variance');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We see that these 150 components account for just over 90% of the variance.\n",
    "That would lead us to believe that using these 150 components, we would recover most of the essential characteristics of the data.\n",
    "To make this more concrete, we can compare the input images with the images reconstructed from these 150 components:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# Compute the components and projected faces\n",
    "pca = RandomizedPCA(150).fit(faces.data)\n",
    "components = pca.transform(faces.data)\n",
    "projected = pca.inverse_transform(components)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pLP4/AaxAgjrBavD03zTWJAIxrR1CEWgq/HgtTR1+LrcsHKX4mGdkLZDYtA8xQtSFwvjI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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11985a5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the results\n",
    "fig, ax = plt.subplots(2, 10, figsize=(10, 2.5),\n",
    "                       subplot_kw={'xticks':[], 'yticks':[]},\n",
    "                       gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
    "for i in range(10):\n",
    "    ax[0, i].imshow(faces.data[i].reshape(62, 47), cmap='binary_r')\n",
    "    ax[1, i].imshow(projected[i].reshape(62, 47), cmap='binary_r')\n",
    "    \n",
    "ax[0, 0].set_ylabel('full-dim\\ninput')\n",
    "ax[1, 0].set_ylabel('150-dim\\nreconstruction');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The top row here shows the input images, while the bottom row shows the reconstruction of the images from just 150 of the ~3,000 initial features.\n",
    "This visualization makes clear why the PCA feature selection used in [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb) was so successful: although it reduces the dimensionality of the data by nearly a factor of 20, the projected images contain enough information that we might, by eye, recognize the individuals in the image.\n",
    "What this means is that our classification algorithm needs to be trained on 150-dimensional data rather than 3,000-dimensional data, which depending on the particular algorithm we choose, can lead to a much more efficient classification."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Principal Component Analysis Summary\n",
    "\n",
    "In this section we have discussed the use of principal component analysis for dimensionality reduction, for visualization of high-dimensional data, for noise filtering, and for feature selection within high-dimensional data.\n",
    "Because of the versatility and interpretability of PCA, it has been shown to be effective in a wide variety of contexts and disciplines.\n",
    "Given any high-dimensional dataset, I tend to start with PCA in order to visualize the relationship between points (as we did with the digits), to understand the main variance in the data (as we did with the eigenfaces), and to understand the intrinsic dimensionality (by plotting the explained variance ratio).\n",
    "Certainly PCA is not useful for every high-dimensional dataset, but it offers a straightforward and efficient path to gaining insight into high-dimensional data.\n",
    "\n",
    "PCA's main weakness is that it tends to be highly affected by outliers in the data.\n",
    "For this reason, many robust variants of PCA have been developed, many of which act to iteratively discard data points that are poorly described by the initial components.\n",
    "Scikit-Learn contains a couple interesting variants on PCA, including ``RandomizedPCA`` and ``SparsePCA``, both also in the ``sklearn.decomposition`` submodule.\n",
    "``RandomizedPCA``, which we saw earlier, uses a non-deterministic method to quickly approximate the first few principal components in very high-dimensional data, while ``SparsePCA`` introduces a regularization term (see [In Depth: Linear Regression](05.06-Linear-Regression.ipynb)) that serves to enforce sparsity of the components.\n",
    "\n",
    "In the following sections, we will look at other unsupervised learning methods that build on some of the ideas of PCA."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<!--NAVIGATION-->\n",
    "< [In-Depth: Decision Trees and Random Forests](05.08-Random-Forests.ipynb) | [Contents](Index.ipynb) | [In-Depth: Manifold Learning](05.10-Manifold-Learning.ipynb) >\n",
    "\n",
    "<a href=\"https://colab.research.google.com/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/05.09-Principal-Component-Analysis.ipynb\"><img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open and Execute in Google Colaboratory\"></a>\n"
   ]
  }
 ],
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